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Dirichlet-Type Problems for Certain Beltrami Equations

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Abstract

In this paper, we shall be interested in solving Dirichlet-type problems for solutions of certain classes of Beltrami equations, to be called \(\beta -\)analytic. Orthogonal decomposition of the corresponding Sobolev space as well as the ortho-projections onto the subspaces of theses decompositions are obtained. Analytic representation formulas for the underlying solutions in terms of integral operators are established.

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Acknowledgements

J. Bory-Reyes was partially supported by the Instituto Politécnico Nacional in the framework of SIP programs through the Grant 20200169.

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Authors and Affiliations

  1. ESIME-Zacatenco, Instituto Politécnico Nacional, 07738, Mexico City, Mexico

    J. Bory-Reyes

  2. Department of Mathematics, Faculty of Science, University of Ostrava, Ostrava, Czechia

    D. Barseghyan & B. Schneider

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  1. J. Bory-Reyes
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  2. D. Barseghyan
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  3. B. Schneider
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Correspondence to B. Schneider.

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All authors contributed equally to the manuscript and typed, read, and approved the final form of the manuscript, which is the result of an intensive collaboration.

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Bory-Reyes, J., Barseghyan, D. & Schneider, B. Dirichlet-Type Problems for Certain Beltrami Equations . Mediterr. J. Math. 18, 103 (2021). https://doi.org/10.1007/s00009-021-01760-2

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